Rendering with NN Interpolation
Deactivating AA and MipMap + Interpolation is the right thing to do. The filters are used with interpolation. The bigger the filter size the smoother the result becomes. But since you don't want any smoothness you should deactivate interpolation. That way you can forget about filters.

Nevertheless Blender seems to sample textures internally with some interpolation.

As a workaround you could use an image manipulation program like GIMP or Photoshop and reduce the colors there. In GIMP you can do it like this: Image > Mode > Indexed.

To automate this task for multiple images you can use BIMP. It is GIMP plugin which is probably already installed. You can find it in File > Batch Image Manipulation...
You can use the filter called "gimp-image-convert-indexed"